A teacher is choosing between two options for a class field trip to an orchard.

Question

At orchard A, admission costs $9 per person, and 3 chaperones are required.
At Orchard B, the cost is $10 per person, but only 1 chaperone is required
At each orchard, the same price applies to both chaperones and students

To help her compare the cost of her two options, the teacher first writes the equation 9 (n + 3) = 10 (n + 1), and then she writes the inequality 9 (n + 3) < 10 (n + 1)

options for the blanks:
True
Or false

Answer 1

Let's analyze the situation:

1. The teacher is comparing the total cost of the trip to Orchard A and Orchard B.

2. For Orchard A, the total cost is given by the equation: \[ \text{Cost} = 9(n + 3) \] where \( n \) is the number of students and 3 chaperones are required.

3. For Orchard B, the total cost is: \[ \text{Cost} = 10(n + 1) \] where 1 chaperone is required.

Now, the two statements made by the teacher involve:

1. The equation \( 9(n + 3) = 10(n + 1) \):

   • This equation is true if we want to find the point at which the total costs of both orchards are equal.

2. The inequality \( 9(n + 3) < 10(n + 1) \):

   • This inequality suggests that the teacher is looking for conditions under which Orchard A is cheaper than Orchard B.

Both statements are mathematically sound and represent valid comparisons of costs based on the requirements for each orchard.

So to fill in the blanks:

• The equation \( 9(n + 3) = 10(n + 1) \) is True because it represents when the costs are equal.
• The inequality \( 9(n + 3) < 10(n + 1) \) is also True because it represents when Orchard A is cheaper than Orchard B.

Thus, the answer is: True, True